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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsProperties of Vector ArithmeticsProperties of Vector Multiplication by Scalar

### Distributive over Scalar Addition

In this page, The property, Multiplication of vector is distributive over scalar addition, is explained.

click on the content to continue..

What does 'distribute' mean? • to trouble or disturb
• to give to many
• to give to many

The answer is 'to give to many'.

Considering that a vector has components as real numbers, Given that vec p = ai+bj+ck and lambda + mu where a,b,c,lambda,mu in bbb R, What will be the result of (lambda + mu) vec p? • scalar
• lambda vec p + mu vec p
• lambda vec p + mu vec p
• lambda + mu vec p

The answer is 'lambda vec p + mu vec p'. This can be proven by multiplying the components individually by the scalar and using vector addition properties.

•  A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.

Distributive Over scalar addition: Given scalars lambda,mu and vector vec p,
(lambda+mu)vec p = lambda vec p + mu vec p

Solved Exercise Problem:

Given that vec p = 3 vec q and vec r = 2 vec q, which of the following equals 7 vec q?

• vec p + vec r
• vec p + 2 vec r
• vec p + 2 vec r
• vec p - vec r
• vec r - vec p

The answer is 'vec p + 2 vec r'

slide-show version coming soon